Design of Antennas for Handheld DVB-H ... - Lunds tekniska högskola

A resonator can be modelled as a parallel resonance circuit, as shown in figure
2.10.
Figure 2.10. Parallel resonance circuit.
The total energy stored in the resonance structure, is the average energy stored in
the capacitance C added with the average energy stored in the inductance L. These
definitions give the following formula to calculate the resonance frequency [24].
f r
1
= (2.9)
2π
LC
2.3.4 Quality Factor
The quality factor describes the ratio between energy stored and energy lost in a
resonator circuit per unit time. There are numerous definitions of Q, but the most
fundamental one is
Maximum energy stored in the network
Q = 2π
*
(2.10)
energy dissipated per cycle
Note that the Q is dimensionless and that it is fundamental because it does not
care about what stores or dissipates the energy. For that reason it applies perfectly
well to both resonant and non-resonant systems. Therefore it is appropriate to
characterise a RC circuit, or even a single component, by the Q [25].
The quality factor for the circuit in figure 2.10, according to formula 2.2 is
ωrW
ωrC
1
Q = = =
(2.11)
P G G * ω * L
l
r
Where ω r is the angular resonant frequency, W is the energy stored and Pl is
power loss in a resonator structure.
The total loss can be divided into several load components, where each of them
can be described by different quality factors. The total quality factor is called
loaded quality factor (Ql) and describes the total loss and can be divided into the
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